Algorithm Design Techniques

Algorithm design techniques are essential for solving complex problems efficiently.

There are various algorithm design techniques that we can utilize depending on the problem at hand. Two popular techniques are divide and conquer and dynamic programming.

Divide and conquer involves breaking down a problem into smaller subproblems, solving each subproblem independently, and combining the solutions to solve the original problem.

Dynamic programming is an optimization technique that solves a problem by breaking it down into overlapping subproblems and solving each subproblem only once, storing the results for future use.

Let's take a look at an example of finding the Greatest Common Divisor (GCD) of two numbers using the Euclidean algorithm:

1class Main {
2  public static void main(String[] args) {
3    int num1 = 9;
4    int num2 = 6;
5    int gcd = findGCD(num1, num2);
6    System.out.println("The GCD of " + num1 + " and " + num2 + " is " + gcd);
7  }
8
9  public static int findGCD(int a, int b) {
10    if (b == 0) {
11      return a;
12    }
13
14    return findGCD(b, a % b);
15  }
16}

In this example, we use the Euclidean algorithm to find the GCD of two numbers by repeatedly dividing the larger number by the smaller number until the remainder becomes zero. The GCD is the remainder obtained in the previous step.

Understanding algorithm design techniques allows us to approach problems systematically and design efficient solutions.

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class Main {

  public static void main(String[] args) {

    // Replace with your Java logic here

    int num1 = 9;

    int num2 = 6;

    int gcd = findGCD(num1, num2);

    System.out.println("The GCD of " + num1 + " and " + num2 + " is " + gcd);

  }

​

  public static int findGCD(int a, int b) {

    if (b == 0) {

      return a;

    }

​

    return findGCD(b, a % b);

  }

}